Remove skin from chicken. In a large skillet heat oil. Brown chicken in hot oil over medium heat about 5 minutes, turning chicken to brown evenly. Drain fat. Add broth, wine, garlic, dried rosemary (if using), salt, and black pepper to chicken in skillet. Bring to boiling; reduce heat. Cover and simmer about 20 minutes.
Add tomatoes, sweet peppers, and mushrooms to skillet. Simmer, covered, 15 minutes more or until chicken is tender and no longer pink. Transfer chicken to a serving dish, reserving vegetables and cooking liquid in skillet. Cover chicken with foil to keep warm.
In a small bowl combine the cornstarch, water, and fresh rosemary (if using); stir into mixture in skillet. Cook and stir until thickened and bubbly. Cook and stir for 2 minutes more. Spoon vegetables and sauce around chicken. Serve with noodles or rice. Makes 4 servings.